Correzione post-reconstruction voxel-by-voxel dell'Effetto di Volume Parziale in imaging emissivo

La tesi riguarda la correzione dell'Effetto di Volume Parziale in imaging emissivo. In particolare sono state considerate tecniche di correzione voxel-by-voxel basate su metodi iterativi e analitici. Lo studio è stato effettuato su una tomografia SPECT del fantoccio NEMA

POISSON IMAGE RECONSTRUCTION WITH TOTAL VARIATION REGULARIZATION

This paper describes an optimization framework for reconstructing nonnegative image intensities from linear projections contaminated with Poisson noise. Such Poisson inverse problems arise in a variety of applications, ranging from medical imaging to astronomy. A total variation regularization term is used to counter the ill-posedness of the inverse problem and results in reconstructions that are piecewise smooth. The proposed algorithm sequentially approximates the objective function with a regularized quadratic surrogate which can easily be minimized. Unlike alternative methods, this approach ensures that the natural nonnegativity constraints are satisfied without placing prohibitive restrictions on the nature of the linear projections to ensure computational tractability. The resulting algorithm is computationally efficient and outperforms similar methods using wavelet-sparsity or partition-based regularization. Index Terms — Photon-limited imaging, Poisson noise, total variation, convex optimization, sparse approximatio